Question Number 29463 by NECx last updated on 09/Feb/18 $${An}\:{object}\:{undergoes}\:{constant} \\ $$$${acceleration}\:{after}\:{starting}\:{from} \\ $$$${rest}\:{and}\:{then}\:{travels}\:\mathrm{5}{m}\:{in}\:{the} \\ $$$${first}\:{second}.{Determine}\:{how}\:{far} \\ $$$${it}\:{will}\:{go}\:{in}\:{the}\:{next}\:{second}. \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{5}{m}\:\:{b}\right)\mathrm{10}{m}\:{c}\right)\mathrm{20}{m}\:{d}\right)\mathrm{5}{m} \\ $$$$ \\ $$$$ \\…
Question Number 29464 by NECx last updated on 09/Feb/18 $${An}\:{arrow}\:{is}\:{projected}\:{straight} \\ $$$${upwards}\:{at}\:{a}\:{speed}\:{of}\:\mathrm{100}{m}/{s}. \\ $$$${With}\:{what}\:{speed}\:{will}\:{it}\:{return}\:{to} \\ $$$${the}\:{ground}\:{if}\:{air}\:{resistance}\:{is} \\ $$$${ignored}? \\ $$ Answered by mrW2 last updated…
Question Number 29418 by ajfour last updated on 08/Feb/18 Commented by ajfour last updated on 08/Feb/18 $${If}\:{sphere}\:\left({blue}\right)\:{starts}\:{rolling} \\ $$$${down}\:{from}\:{top}\:{of}\:{a}\:{semi}\:{cylindrical} \\ $$$${surface}\:\left({motion}\:{just}\:{initiated}\:{here}\right), \\ $$$${and}\:{coefficient}\:{of}\:{friction}\:{between} \\ $$$${them}\:{is}\:\boldsymbol{\mu},\:{find}\:{at}\:{what}\:{angle}\:\boldsymbol{\theta}…
Question Number 29400 by ajfour last updated on 08/Feb/18 Commented by ajfour last updated on 08/Feb/18 $${Find}\:\boldsymbol{{b}}\:{in}\:{terms}\:{of}\:\boldsymbol{{a}},\boldsymbol{{u}},\boldsymbol{\alpha},\:{and}\:\boldsymbol{{e}}\:. \\ $$$$\left(\boldsymbol{{e}}\:{being}\:{the}\:{coefficient}\:{of}\right. \\ $$$$\left.{restitution}\right)\: \\ $$ Answered by…
Question Number 29359 by NECx last updated on 08/Feb/18 $${On}\:{a}\:{two}\:{lane}\:{road},{car}\:{A}\:{is} \\ $$$${travelling}\:{with}\:{a}\:{speed}\:{of}\:\mathrm{36}{km}/{h}. \\ $$$${Two}\:{cars}\:{B}\:{and}\:{C}\:{approach}\:{A}\:{in} \\ $$$${opposite}\:{directions}\:{with}\:{a}\:{speed}\:{of} \\ $$$$\mathrm{54}{km}/{h}\:{each}.{At}\:{a}\:{certain}\:{instant}, \\ $$$${when}\:{the}\:{distance}\:{AB}\:{is}\:{equal} \\ $$$${to}\:{AC},{both}\:{being}\:\mathrm{1}{km},{B}\:{decides} \\ $$$${to}\:{overtake}\:{A}\:{before}\:{C}\:{does}.{What} \\…
Question Number 29360 by NECx last updated on 08/Feb/18 $${Two}\:{stones}\:{are}\:{thrown}\:{up}\: \\ $$$${simultaneously}\:{from}\:{the}\:{edge}\:{of} \\ $$$${a}\:{cliff}\:\mathrm{200}{m}\:{high}\:{with}\:{initial} \\ $$$${speeds}\:{of}\:\mathrm{15}{ms}^{−\mathrm{1}} \:{and}\:\mathrm{30}{ms}^{−\mathrm{1}} . \\ $$$${Verify}\:{that}\:{the}\:{graph}\:{shown} \\ $$$${below}\:{correctly}\:{represents}\:{the} \\ $$$${time}\:{variation}\:{of}\:{the}\:{relative} \\…
Question Number 29322 by ajfour last updated on 07/Feb/18 Commented by ajfour last updated on 07/Feb/18 $${Find}\:{acceleration}\:{of}\:{sphere}\:{as} \\ $$$${a}\:{function}\:{of}\:{angle}\:\theta. \\ $$$${System}\:{is}\:{released}\:{at}\:\theta=\:\theta_{\mathrm{0}} \:\left(<\mathrm{90}°\right)\:; \\ $$$$\left({All}\:{surfaces}\:{are}\:{frictionless}\right). \\…
Question Number 29314 by Tinkutara last updated on 07/Feb/18 Commented by mrW2 last updated on 08/Feb/18 $${thanks}\:{sir}! \\ $$ Commented by ajfour last updated on…
Question Number 29273 by ajfour last updated on 06/Feb/18 Commented by ajfour last updated on 06/Feb/18 $${Ice}\:{cube}\:{melts}\:{due}\:{to}\:{friction}, \\ $$$${as}\:{it}\:{slides}\:{down}\:{a}\:{rough}\:{incline}. \\ $$$$\frac{{dm}}{{dx}}\:=−\frac{{f}}{{s}\bigtriangleup{T}_{\mathrm{0}} }\:\:\:\:\left({f}\:{is}\:{force}\:{of}\:{friction}\right) \\ $$$${s}\:{the}\:{specific}\:{heat}\:{of}\:{ice}\:{and} \\…
Question Number 29260 by NECx last updated on 06/Feb/18 $${The}\:{eriodic}\:{time}\:{of}\:{a}\:{simple} \\ $$$${pendulum}\:{is}\:{given}\:{by}\:{T}=\mathrm{2}\pi\sqrt{\frac{{L}}{{g}}}. \\ $$$${if}\:{L}=\mathrm{100}\pm\mathrm{0}.\mathrm{1}{cm}\left({s}.{e}\right)\:{and}\:{the} \\ $$$${time}\:{s}\:{for}\:\mathrm{10}\:{ossilations}\:{are}: \\ $$$$\mathrm{48}.\mathrm{2},\mathrm{48}.\mathrm{2},\mathrm{48}.\mathrm{7},\mathrm{48}.\mathrm{5},\mathrm{48}.\mathrm{4},\mathrm{48}.\mathrm{2},\mathrm{48}.\mathrm{4}, \\ $$$$\mathrm{48}.\mathrm{6},\mathrm{48}.\mathrm{5},\mathrm{48}.\mathrm{2}. \\ $$$${calcukate}\:{g}\:{and}\:{the}\:{standard} \\ $$$${error}\:{involved}. \\…